Which of these numbers is prime? ${53,\ 57,\ 82,\ 93,\ 99}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 53 are 1 and 53. The factors of 57 are 1, 3, 19, and 57. The factors of 82 are 1, 2, 41, and 82. The factors of 93 are 1, 3, 31, and 93. The factors of 99 are 1, 3, 9, 11, 33, and 99. Thus, 53 is a prime number.